Partial Galaxy Clustering : An Estimator Incorporating Probabilistic - - PowerPoint PPT Presentation

Partial Galaxy Clustering: An Estimator Incorporating Probabilistic Distance Measurements

Humna Awan Advisor: Eric Gawiser Rutgers University, Dept. of Physics & Astronomy April 20, 2018 SCLSS, Oxford

De-Projection

Consider how the correlations in the contaminated subsamples relate to the true ones: Assumes the classification probabilities can be represented by their sample averages.

Humna Awan SCLSS 2018

De-Projection

Consider how the correlations in the contaminated subsamples relate to the true ones: Assumes the classification probabilities can be represented by their sample averages. => De-projected LS estimators for the auto/cross-correlations:

Humna Awan SCLSS 2018

Possible improvement to assumptions about contamination?

Humna Awan SCLSS 2018

Estimators that incorporate uncertainty in galaxy radial positions

Humna Awan SCLSS 2018

Probability-Weighted Estimator

Marked correlations: extract features in correlations. Weigh each galaxy by its classification probability! ⇒ Consider *all* galaxies, without divisions into subsamples. ⇒ Probability-weighted estimator where

Humna Awan SCLSS 2018

Probability-Weighted Estimator: De-Biasing

is biased: need to de-bias to get We have ⇒ Can de-bias individual histograms, ,

Humna Awan SCLSS 2018

Probability-Weighted Estimator: De-Biasing

Humna Awan SCLSS 2018

After all the algebra and some simplifications, we have with [M], [C] are calculable given the weights.

Probability-Weighted Estimator: De-Biasing

Humna Awan SCLSS 2018

Test

We apply the estimators to a HETDEX mock catalog**

• 2-sample case: either one is a contaminant w.r.t the other.
• Can construct a probabilistic classifier assigning each observed galaxy of

type A a probability of being type B:

• Use the probabilities in the estimators!

Renders each galaxy’s existence in a sample a probabilistic existence in each distance bin.

• Example realization: 719,881 true LAEs and 465,104 true [OII] emitters
• Implement 10% LAE sample contamination; 6% incompleteness to create
• bserved catalogs.
• Well-behaved, unbiased classification probability distributions.
• Jackknife to get the variance (while work in progress for analytical

expressions)

*Thanks to Chi-Ting Chiang.

Humna Awan SCLSS 2018

Results: LAE auto-correlation

Weights for each galaxy= classification probability Jackknife errors

Humna Awan SCLSS 2018 Awan & Gawiser, in prep

Results: LAE auto-correlation

Weights for each galaxy= classification probability New estimator gives unbiased result => de-biasing is working. Variance is comparable with simplest weights.

Humna Awan SCLSS 2018 Awan & Gawiser, in prep

Summary

• Improved galaxy clustering estimators:
• Needed to account for measurement uncertainties directly.
• Photo-z surveys, e.g. LSST: ~9-contaminant case. 2D.
• Emission-line surveys, e.g. HETDEX: 1-contaminant case. 3D.
• Discussed here: probability-weighted estimator
• Uses probabilistic distance measurements.
• Have the infrastructure to test different weights.

Current Work

• Optimize weights to minimize/reduce variance.
• Apply the estimators to a photo-z catalog: 2D applicable.
• De-biasing+variance for general classification prob. distributions.
• Extend 2-sample methods to 3-sample (then generalizable?).

Future

• Estimators for 3D correlations.

Thanks to RDI2 Fellowship for Excellence in Computation and Data Science 2017-2018

Humna Awan SCLSS 2018

Galaxy Correlation Functions

2pt galaxy autocorrelation function w(θ) (angular= 2D)

• A common statistic to study galaxy clustering
• Measures excess probability of finding a galaxy at an

angular distance θ from another galaxy in comparison with a random distribution:

Humna Awan SCLSS 2018

(2D) 2pt galaxy autocorrelation function w(θ)

• Landy-Szalay estimator:

DD, DR, RR are histograms. Explicitly, e.g. , where is the Heaviside step function.

Galaxy Clustering: Traditional Estimator

Humna Awan SCLSS 2018

Galaxy Clustering: Traditional Estimator

(2D) 2pt galaxy autocorrelation function w(θ)

• Landy-Szalay estimator:

Unbiased estimator but requires a “clean” sample ⇒ Need to make assumptions about the contamination in the sample -- limits utilizing all the available information. Why is it a problem?

Humna Awan SCLSS 2018

Results: LAE auto-correlation

Sanity check: Weights for each galaxy= 1/(classification probability) Expect things to not work, and they don’t.

Humna Awan SCLSS 2018 Awan & Gawiser, in prep